Problem: You are given an integer N.

Construct any one N-by-N matrix a that satisfies the conditions below. It can be proved that a solution always exists under the constraints of this problem.

* 1 \leq a_{i,j} \leq 10^{15}
* a_{i,j} are pairwise distinct integers.
* There exists a positive integer m such that the following holds: Let x and y be two elements of the matrix that are vertically or horizontally adjacent. Then, {\rm max}(x,y) {\rm mod} {\rm min}(x,y) is always m.

Constraints

* 2 \leq N \leq 500

Input

Input is given from Standard Input in the following format:


N


Output

Print your solution in the following format:


a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Output

Print your solution in the following format:


a_{1,1} ... a_{1,N}
:
a_{N,1} ... a_{N,N}

Example

Input

2


Output

4 7
23 10

Solution (in CPP):

Solution:
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
#define MN 500
#define MX 5000
int u[MX+5],p[MX+5],pn;
ll a[MN+5][MN+5];
map<ll,int> mp;
ll gcd(ll x,ll y){return y?gcd(y,x%y):x;}
int main()
{
	int n,i,j,k,x,y;
	for(i=2;i<=MX;++i)
	{
		if(!u[i])p[++pn]=i;
		for(j=1;i*p[j]<=MX;++j)if(u[i*p[j]]=1,i%p[j]==0)break;
	}
	for(i=2;i<=MN+MN;i+=2)for(j=-MN;j<=MN;j+=2)
	{
		x=(i+j)/2;y=(i-j)/2;
		if(x<1||x>MN||y<1||y>MN)continue;
		for(k=1;mp[2*p[i/2]*p[(j+MN)/2]*k]++;++k);
		a[x][y]=2*p[i/2]*p[(j+MN)/2]*k;
	}
	for(i=1;i<=MN;++i)for(j=1;j<=MN;++j)if(!a[i][j])
	{
		ll x=1;
		if(i>1)x=x/gcd(x,a[i-1][j])*a[i-1][j];
		if(i<MN)x=x/gcd(x,a[i+1][j])*a[i+1][j];
		if(j>1)x=x/gcd(x,a[i][j-1])*a[i][j-1];
		if(j<MN)x=x/gcd(x,a[i][j+1])*a[i][j+1];
		for(k=1;mp[x*k+1]++;++k);
		a[i][j]=x*k+1;
	}
	scanf("%d",&n);
	for(i=1;i<=n;++i,puts(""))for(j=1;j<=n;++j)printf("%lld ",a[i][j]);
}